Mathematics Assessment

Mathematics Assessment

PART A: Break Even Analysis

Question 1

Break Even Analysis

The threshold of profitability reflects a situation in which revenues from sales cover fixed costs and variable costs the company. Prerequisite for calculating the break-even point is the division of the costs of undertaking the fixed costs (e.g. depreciation is the fixed cost) and variable costs (such as energy used in manufacturing, materials or wages of production workers, as long as they grow with the increase of production).

Break-even point can be expressed quantitatively (ie how many units of the product you need to sell), or value (i.e. the value must reach this sale). The company does not break even or loss-is non-profit, profit is equal to 0 But more importantly, the break-even cash flow is equal to depreciation, as it is a non-cash expense (not related to its cash flow from the company).

Break-even point is calculated using the following formulas:

BEP quantitative = (fixed costs) / (price - variable cost per unit)

BEP value = quantity * price, or (KS / margin unit) * price

BEP percentage = (fixed costs) / (demand) * 100

The blue line in graph shows the expenditure function as it is given that the expenditure contains fixed cost as well and the intercept of the blue line represents the fixed cost whereas the pink line represents the income function.

(i) In small businesses, we usually include land as the major fixed cost. Further, technological instruments like machines and computers are also included in fixed costs. Further, in short term labor is considered as the fixed cost.

(ii) The fixed cost in the given scenario is 500 from the graph. The intercept of the expenditure function is known as the fixed cost.

Fixed cost = 500

Total cost for 5 stapling machines = 600

Cost of producing 5 stapling machines = 600 - 500 = 100

Cost of producing 1 stapling machine = 100 / 5 = 20

From the income function, 5 stapling machines earns 200

Selling price for each stapling machine = 200 / 5 = 40

From the graph, they need 25 stapling machines to break even the overall cost.

Income from 10 stapling machines = 400

Expenditures from 10 stapling machines = 700

Total loss in a day, if 10 stapling machines are manufactured and sold = 700 - 400 = 300

Revenue Function ( Y = 40*x ,

Where Y is the revenue obtained by selling X stapling machines

Expenditure Function ( Z = 500 + 20*X

Where Z ...